Solving quantifier-free non-linear real arithmetic (NRA) problems is a computationally hard task. To tackle this problem, prior work proposed a promising approach based on gradient descent. In this work, we extend their ideas and combine LLMs and GPU acceleration to obtain an efficient technique. We have implemented our findings in the novel SMT solver GANRA (GPU Accelerated solving of Nonlinear Real Arithmetic problems). We evaluate GANRA on two different NRA benchmarks and demonstrate significant improvements over the previous state of the art. In particular, on the Sturm-MBO benchmark, we can prove satisfiability for more than five times as many instances in less than 1/20th of the previous state-of-the-art runtime.

Rb-82 dynamic cardiac PET imaging is widely used for the clinical diagnosis of coronary artery disease (CAD), but its short half-life results in high noise levels that degrade dynamic frame quality and parametric imaging. The lack of paired clean-noisy training data, rapid tracer kinetics, and frame-dependent noise variations further limit the effectiveness of existing deep learning denoising methods. We propose DECADE (A Temporally-Consistent Unsupervised Diffusion model for Enhanced Rb-82 CArdiac PET DEnoising), an unsupervised diffusion framework that generalizes across early- to late-phase dynamic frames. DECADE incorporates temporal consistency during both training and iterative sampling, using noisy frames as guidance to preserve quantitative accuracy. The method was trained and evaluated on datasets acquired from Siemens Vision 450 and Siemens Biograph Vision Quadra scanners. On the Vision 450 dataset, DECADE consistently produced high-quality dynamic and parametric images with reduced noise while preserving myocardial blood flow (MBF) and myocardial flow reserve (MFR). On the Quadra dataset, using 15%-count images as input and full-count images as reference, DECADE outperformed UNet-based and other diffusion models in image quality and K1/MBF quantification. The proposed framework enables effective unsupervised denoising of Rb-82 dynamic cardiac PET without paired training data, supporting clearer visualization while maintaining quantitative integrity.

Long-term language-guided referring in fixed-view videos is challenging: the referent may be occluded or leave the scene for long intervals and later re-enter, while framewise referring pipelines drift as re-identification (ReID) becomes unreliable. AR2-4FV leverages background stability for long-term referring. An offline Anchor Bank is distilled from static background structures; at inference, the text query is aligned with this bank to produce an Anchor Map that serves as persistent semantic memory when the referent is absent. An anchor-based re-entry prior accelerates re-capture upon return, and a lightweight ReID-Gating mechanism maintains identity continuity using displacement cues in the anchor frame. The system predicts per-frame bounding boxes without assuming the target is visible in the first frame or explicitly modeling appearance variations. AR2-4FV achieves +10.3% Re-Capture Rate (RCR) improvement and -24.2% Re-Capture Latency (RCL) reduction over the best baseline, and ablation studies further confirm the benefits of the Anchor Map, re-entry prior, and ReID-Gating.

A geometric hallucination taxonomy distinguishes three failure types -- center-drift (Type~1), wrong-well convergence (Type~2), and coverage gaps (Type~3) -- by their signatures in embedding cluster space. Prior work found Types~1 and~2 indistinguishable in full-dimensional contextual measurement. We address this through PCA-whitening and eigenspectrum decomposition on GPT-2-small, using multi-run stability analysis (20 seeds) with prompt-level aggregation. Whitening transforms the micro-signal regime into a space where peak cluster alignment (max\_sim) separates Type~2 from Type~3 at Holm-corrected significance, with condition means following the taxonomy's predicted ordering: Type~2 (highest commitment) $>$ Type~1 (intermediate) $>$ Type~3 (lowest). A first directionally stable but underpowered hint of Type~1/2 separation emerges via the same metric, generating a capacity prediction for larger models. Prompt diversification from 15 to 30 prompts per group eliminates a false positive in whitened entropy that appeared robust at the smaller set, demonstrating prompt-set sensitivity in the micro-signal regime. Eigenspectrum decomposition localizes this artifact to the dominant principal components and confirms that Type~1/2 separation does not emerge in any spectral band, rejecting the spectral mixing hypothesis. The contribution is threefold: whitening as preprocessing that reveals cluster commitment as the theoretically correct separating metric, evidence that the Type~1/2 boundary is a capacity limitation rather than a measurement artifact, and a methodological finding about prompt-set fragility in near-saturated representation spaces.

Financial time-series forecasting is a high-stakes problem where regime shifts and shocks make point-accurate yet overconfident models dangerous. We propose Uncertainty-Gated Generative Modeling (UGGM), which treats uncertainty as an internal control signal that gates (i) representation via gated reparameterization, (ii) propagation via similarity and confidence routing, and (iii) generation via uncertainty-controlled predictive distributions, together with uncertainty-driven regularization and calibration to curb miscalibration. Instantiated on Weak Innovation AutoEncoder (WIAE-GPF), our UG-WIAE-GPF significantly improves risk-sensitive forecasting, delivering a 63.5\% MSE reduction on NYISO (0.3508 $\rightarrow$ 0.1281), with improved robustness under shock intervals (mSE: 0.2739 $\rightarrow$ 0.1748).

Precise object placement remains underexplored in aerial manipulation, where most systems rely on predefined target coordinates and focus primarily on grasping and control. Specifying exact placement poses, however, is cumbersome in real-world settings, where users naturally communicate goals through language. In this work, we present AeroPlace-Flow, a training-free framework for language-grounded aerial object placement that unifies visual foresight with explicit 3D geometric reasoning and object flow. Given RGB-D observations of the object and the placement scene, along with a natural language instruction, AeroPlace-Flow first synthesizes a task-complete goal image using image editing models. The imagined configuration is then grounded into metric 3D space through depth alignment and object-centric reasoning, enabling the inference of a collision-aware object flow that transports the grasped object to a language and contact-consistent placement configuration. The resulting motion is executed via standard trajectory tracking for an aerial manipulator. AeroPlace-Flow produces executable placement targets without requiring predefined poses or task-specific training. We validate our approach through extensive simulation and real-world experiments, demonstrating reliable language-conditioned placement across diverse aerial scenarios with an average success rate of 75% on hardware.

Federated Graph Learning (FedGL) is vulnerable to malicious attacks, yet developing a truly effective and stealthy attack method remains a significant challenge. Existing attack methods suffer from low attack success rates, high computational costs, and are easily identified and smoothed by defense algorithms. To address these challenges, we propose \textbf{FedShift}, a novel two-stage "Hide and Find" distributed adversarial attack. In the first stage, before FedGL begins, we inject a learnable and hidden "shifter" into part of the training data, which subtly pushes poisoned graph representations toward a target class's decision boundary without crossing it, ensuring attack stealthiness during training. In the second stage, after FedGL is complete, we leverage the global model information and use the hidden shifter as an optimization starting point to efficiently find the adversarial perturbations. During the final attack, we aggregate these perturbations from multiple malicious clients to form the final effective adversarial sample and trigger the attack. Extensive experiments on six large-scale datasets demonstrate that our method achieves the highest attack effectiveness compared to existing advanced attack methods. In particular, our attack can effectively evade 3 mainstream robust federated learning defense algorithms and converges with a time cost reduction of over 90\%, highlighting its exceptional stealthiness, robustness, and efficiency.

This work investigated the capabilities of different models, including the Llama-3 series of models and CHATGPT, with different forms of expression in solving discrete optimization problems by testing natural language datasets. In contrast to formal datasets with a limited scope of parameters, our dataset included a variety of problem types in discrete optimization problems and featured a wide range of parameter magnitudes, including instances with large parameter sets, integrated with augmented data. It aimed to (1) provide an overview of LLMs' ability in large-scale problems, (2) offer suggestions to those who want to solve discrete optimization problems automatically, and (3) regard the performance as a benchmark for future research. These datasets included original, expanded and augmented datasets. Among these three datasets, the original and augmented ones aimed for evaluation while the expanded one may help finetune a new model. In the experiment, comparisons were made between strong and week models, CoT methods and No-CoT methods on various datasets. The result showed that stronger model performed better reasonably. Contrary to general agreement, it also showed that CoT technique was not always effective regarding the capability of models and disordered datasets improved performance of models on easy to-understand problems, even though they were sometimes with high variance, a manifestation of instability. Therefore, for those who seek to enhance the automatic resolution of discrete optimization problems, it is recommended to consult the results, including the line charts presented in the Appendix, as well as the conclusions drawn in this study for relevant suggestions.

Large language models (LLMs) such as GPT and Gemini have demonstrated remarkable capabilities in contextual understanding and reasoning. The strong performance of LLMs has sparked growing interest in leveraging them to automate tasks traditionally dependent on human expertise. Recently, LLMs have been integrated into intelligent agents capable of operating structural analysis software (e.g., OpenSees) to construct structural models and perform analyses. However, existing LLMs are limited in handling multi-step structural modeling due to frequent hallucinations and error accumulation during long-sequence operations. To this end, this study presents a novel multi-agent architecture to automate the structural modeling and analysis using OpenSeesPy. First, problem analysis and construction planning agents extract key parameters from user descriptions and formulate a stepwise modeling plan. Node and element agents then operate in parallel to assemble the frame geometry, followed by a load assignment agent. The resulting geometric and load information is translated into executable OpenSeesPy scripts by code translation agents. The proposed architecture is evaluated on a benchmark of 20 frame problems over ten repeated trials, achieving 100% accuracy in 18 cases and 90% in the remaining two. The architecture also significantly improves computational efficiency and demonstrates scalability to larger structural systems.

We test whether LLMs show robust decision biases. Treating models as participants in two-arm bandits, we ran 20000 trials per condition across four decoding configurations. Under symmetric rewards, models amplified positional order into stubborn one-arm policies. Under asymmetric rewards, they exploited rigidly yet underperformed an oracle and rarely re-checked. The observed patterns were consistent across manipulations of temperature and top-p, with top-k held at the provider default, indicating that the qualitative behaviours are robust to the two decoding knobs typically available to practitioners. Crucially, moving beyond descriptive metrics to computational modelling, a hierarchical Rescorla-Wagner-softmax fit revealed the underlying strategies: low learning rates and very high inverse temperatures, which together explain both noise-to-bias amplification and rigid exploitation. These results position minimal bandits as a tractable probe of LLM decision tendencies and motivate hypotheses about how such biases could shape human-AI interaction.

Unlike the predictable scaling laws in natural language processing and computer vision, protein language models (PLMs) scale poorly: for many tasks, models within the same family plateau or even decrease in performance, with mid-sized models often outperforming the largest in the family. We introduce Reverse Distillation, a principled framework that decomposes large PLM representations into orthogonal subspaces guided by smaller models of the same family. The resulting embeddings have a nested, Matryoshka-style structure: the first k dimensions of a larger model's embedding are exactly the representation from the smaller model. This ensures that larger reverse-distilled models consistently outperform smaller ones. A motivating intuition is that smaller models, constrained by capacity, preferentially encode broadly-shared protein features. Reverse distillation isolates these shared features and orthogonally extracts additional contributions from larger models, preventing interference between the two. On ProteinGym benchmarks, reverse-distilled ESM-2 variants outperform their respective baselines at the same embedding dimensionality, with the reverse-distilled 15 billion parameter model achieving the strongest performance. Our framework is generalizable to any model family where scaling challenges persist. Code and trained models are available at https://github.com/rohitsinghlab/plm_reverse_distillation.

Voice interfaces are quickly becoming a common way for people to interact with AI systems. This also brings new security risks, such as prompt injection, social engineering, and harmful voice commands. Traditional security methods rely on converting speech to text and then filtering that text, which introduces delays and can ignore important audio cues. This paper introduces VoiceSHIELD-Small, a lightweight model that works in real time. It can transcribe speech and detect whether it is safe or harmful, all in one step. Built on OpenAI's Whisper-small encoder, VoiceSHIELD adds a mean-pooling layer and a simple classification head. It takes just 90-120 milliseconds to classify audio on mid-tier GPUs, while transcription happens at the same time. Tested on a balanced set of 947 audio clips, the model achieved 99.16 percent accuracy and an F1 score of 0.9865. At the default setting, it missed 2.33 percent of harmful inputs. Cross-validation showed consistent performance (F1 standard deviation = 0.0026). The paper also covers the model's design, training data, performance trade-offs, and responsible use guidelines. VoiceSHIELD is released under the MIT license to encourage further research and adoption in voice AI security.

Greedy algorithms are central to sparse approximation and stage-wise learning methods such as matching pursuit and boosting. It is known that the Power-Relaxed Greedy Algorithm with step sizes $m^{-α}$ may fail to converge when $α>1$ in general Hilbert spaces. In this work, we revisit this phenomenon from a sparse learning perspective. We study realizable regression problems with controlled feature coherence and derive explicit lower bounds on the residual norm, showing that over-decaying step-size schedules induce structural stagnation even in low-dimensional sparse settings. Numerical experiments confirm the theoretical predictions and illustrate the role of feature coherence. Our results provide insight into step-size design in greedy sparse learning.

While few-step generative models have enabled powerful image and video generation at significantly lower cost, generic reinforcement learning (RL) paradigms for few-step models remain an unsolved problem. Existing RL approaches for few-step diffusion models strongly rely on back-propagating through differentiable reward models, thereby excluding the majority of important real-world reward signals, e.g., non-differentiable rewards such as humans' binary likeness, object counts, etc. To properly incorporate non-differentiable rewards to improve few-step generative models, we introduce TDM-R1, a novel reinforcement learning paradigm built upon a leading few-step model, Trajectory Distribution Matching (TDM). TDM-R1 decouples the learning process into surrogate reward learning and generator learning. Furthermore, we developed practical methods to obtain per-step reward signals along the deterministic generation trajectory of TDM, resulting in a unified RL post-training method that significantly improves few-step models' ability with generic rewards. We conduct extensive experiments ranging from text-rendering, visual quality, and preference alignment. All results demonstrate that TDM-R1 is a powerful reinforcement learning paradigm for few-step text-to-image models, achieving state-of-the-art reinforcement learning performances on both in-domain and out-of-domain metrics. Furthermore, TDM-R1 also scales effectively to the recent strong Z-Image model, consistently outperforming both its 100-NFE and few-step variants with only 4 NFEs. Project page: https://github.com/Luo-Yihong/TDM-R1

Efficient multi-UAV exploration under limited communication is severely bottlenecked by inadequate task representation and allocation. Previous task representations either impose heavy communication requirements for coordination or lack the flexibility to handle complex environments, often leading to inefficient traversal. Furthermore, short-horizon allocation strategies neglect spatiotemporal contiguity, causing non-contiguous assignments and frequent cross-region detours. To address this, we propose C$^2$-Explorer, a decentralized framework that constructs a connectivity graph to decompose disconnected unknown components into independent task units. We then introduce a contiguity-driven allocation formulation with a graph-based neighborhood penalty to discourage non-adjacent assignments, promoting more contiguous task sequences over time. Extensive simulation experiments show that C$^2$-Explorer consistently outperforms state-of-the-art (SOTA) baselines, reducing average exploration time by 43.1\% and path length by 33.3\%. Real-world flights further demonstrate the system's feasibility. The code will be released at https://github.com/Robotics-STAR-Lab/C2-Explorer

We study infinite-horizon Constrained Markov Decision Processes (CMDPs) with general policy parameterizations and multi-layer neural network critics. Existing theoretical analyses for constrained reinforcement learning largely rely on tabular policies or linear critics, which limits their applicability to high-dimensional and continuous control problems. We propose a primal-dual natural actor-critic algorithm that integrates neural critic estimation with natural policy gradient updates and leverages Neural Tangent Kernel (NTK) theory to control function-approximation error under Markovian sampling, without requiring access to mixing-time oracles. We establish global convergence and cumulative constraint violation rates of $\tilde{\mathcal{O}}(T^-1/4)$ up to approximation errors induced by the policy and critic classes. Our results provide the first such guarantees for CMDPs with general policies and multi-layer neural critics, substantially extending the theoretical foundations of actor-critic methods beyond the linear-critic regime.

Vision-based motion capture solutions often struggle with occlusions, which result in the loss of critical joint information and hinder accurate 3D motion reconstruction. Other wearable alternatives also suffer from noisy or unstable data, often requiring extensive manual cleaning and correction to achieve reliable results. To address these challenges, we introduce the Masked Motion Diffusion Model (MMDM), a diffusion-based generative reconstruction framework that enhances incomplete or low-confidence motion data using partially available high-quality reconstructions within a Masked Autoencoder architecture. Central to our design is the Kinematic Attention Aggregation (KAA) mechanism, which enables efficient, deep, and iterative encoding of both joint-level and pose-level features, capturing structural and temporal motion patterns essential for task-specific reconstruction. We focus on learning context-adaptive motion priors, specialized structural and temporal features extracted by the same reusable architecture, where each learned prior emphasizes different aspects of motion dynamics and is specifically efficient for its corresponding task. This enables the architecture to adaptively specialize without altering its structure. Such versatility allows MMDM to efficiently learn motion priors tailored to scenarios such as motion refinement, completion, and in-betweening. Extensive evaluations on public benchmarks demonstrate that MMDM achieves strong performance across diverse masking strategies and task settings. The source code is available at https://github.com/jjkislele/MMDM.

In bandwidth-limited online video streaming, videos are usually downsampled and compressed. Although recent online video super-resolution (online VSR) approaches achieve promising results, they are still compute-intensive and fall short of real-time processing at higher resolutions, due to complex motion estimation for alignment and redundant processing of consecutive frames. To address these issues, we propose a compressed-domain-aware network (CDA-VSR) for online VSR, which utilizes compressed-domain information, including motion vectors, residual maps, and frame types to balance quality and efficiency. Specifically, we propose a motion-vector-guided deformable alignment module that uses motion vectors for coarse warping and learns only local residual offsets for fine-tuned adjustments, thereby maintaining accuracy while reducing computation. Then, we utilize a residual map gated fusion module to derive spatial weights from residual maps, suppressing mismatched regions and emphasizing reliable details. Further, we design a frame-type-aware reconstruction module for adaptive compute allocation across frame types, balancing accuracy and efficiency. On the REDS4 dataset, our CDA-VSR surpasses the state-of-the-art method TMP, with a maximum PSNR improvement of 0.13 dB while delivering more than double the inference speed. The code will be released at https://github.com/sspBIT/CDA-VSR.

Understanding spatial affordances -- comprising the contact regions of object interaction and the corresponding contact poses -- is essential for robots to effectively manipulate objects and accomplish diverse tasks. However, existing spatial affordance prediction methods mainly focus on locating the contact regions while delegating the pose to independent pose estimation approaches, which can lead to task failures due to inconsistencies between predicted contact regions and candidate poses. In this work, we propose RoboPCA, a pose-centered affordance prediction framework that jointly predicts task-appropriate contact regions and poses conditioned on instructions. To enable scalable data collection for pose-centered affordance learning, we devise Human2Afford, a data curation pipeline that automatically recovers scene-level 3D information and infers pose-centered affordance annotations from human demonstrations. With Human2Afford, scene depth and the interaction object's mask are extracted to provide 3D context and object localization, while pose-centered affordance annotations are obtained by tracking object points within the contact region and analyzing hand-object interaction patterns to establish a mapping from the 3D hand mesh to the robot end-effector orientation. By integrating geometry-appearance cues through an RGB-D encoder and incorporating mask-enhanced features to emphasize task-relevant object regions into the diffusion-based framework, RoboPCA outperforms baseline methods on image datasets, simulation, and real robots, and exhibits strong generalization across tasks and categories.

The Consistency property between surrogate losses and evaluation metrics has been extensively studied to ensure that minimizing a loss leads to metric optimality. However, the direct relationship between different evaluation metrics remains significantly underexplored. This theoretical gap results in the "Metric Mismatch" frequently observed in industrial applications, where gains in offline validation metrics fail to translate into online performance. To bridge this disconnection, this paper proposes a unified theoretical framework designed to quantify the relationships between metrics. We categorize metrics into different classes to facilitate a comparative analysis across different mathematical forms and interrogates these relationships through Bayes-Optimal Set and Regret Transfer. Through this framework, we provide a new perspective on identifying the structural asymmetry in regret transfer, enabling the design of evaluation systems that are theoretically guaranteed to align offline improvements with online objectives.

Large language model (LLM) agents increasingly operate in settings where a single context window is far too small to capture what has happened, what was learned, and what should not be repeated. Memory -- the ability to persist, organize, and selectively recall information across interactions -- is what turns a stateless text generator into a genuinely adaptive agent. This survey offers a structured account of how memory is designed, implemented, and evaluated in modern LLM-based agents, covering work from 2022 through early 2026. We formalize agent memory as a \emph{write--manage--read} loop tightly coupled with perception and action, then introduce a three-dimensional taxonomy spanning temporal scope, representational substrate, and control policy. Five mechanism families are examined in depth: context-resident compression, retrieval-augmented stores, reflective self-improvement, hierarchical virtual context, and policy-learned management. On the evaluation side, we trace the shift from static recall benchmarks to multi-session agentic tests that interleave memory with decision-making, analyzing four recent benchmarks that expose stubborn gaps in current systems. We also survey applications where memory is the differentiating factor -- personal assistants, coding agents, open-world games, scientific reasoning, and multi-agent teamwork -- and address the engineering realities of write-path filtering, contradiction handling, latency budgets, and privacy governance. The paper closes with open challenges: continual consolidation, causally grounded retrieval, trustworthy reflection, learned forgetting, and multimodal embodied memory.

Spatial registration across different visual modalities is a critical but formidable step in multi-modality image fusion for real-world perception. Although several methods are proposed to address this issue, the existing registration-based fusion methods typically require extensive pre-registration operations, limiting their efficiency. To overcome these limitations, a general cross-modality registration method guided by visual priors is proposed for infrared and visible image fusion task, termed FusionRegister. Firstly, FusionRegister achieves robustness by learning cross-modality misregistration representations rather than forcing alignment of all differences, ensuring stable outputs even under challenging input conditions. Moreover, FusionRegister demonstrates strong generality by operating directly on fused results, where misregistration is explicitly represented and effectively handled, enabling seamless integration with diverse fusion methods while preserving their intrinsic properties. In addition, its efficiency is further enhanced by serving the backbone fusion method as a natural visual prior provider, which guides the registration process to focus only on mismatch regions, thereby avoiding redundant operations. Extensive experiments on three datasets demonstrate that FusionRegister not only inherits the fusion quality of state-of-the-art methods, but also delivers superior detail alignment and robustness, making it highly suitable for infrared and visible image fusion method. The code will be available at https://github.com/bociic/FusionRegister.

Imitation learning has shown strong potential for automating complex robotic manipulation. In medical robotics, ultrasound-guided needle insertion demands precise bimanual coordination, as clinicians must simultaneously manipulate an ultrasound probe to maintain an optimal acoustic view while steering an interventional needle. Automating this asymmetric workflow -- and reliably transferring expert strategies to robots -- remains highly challenging. In this paper, we present the Dual-Arm Interventional Surgical System (DAISS), a teleoperated platform that collects high-fidelity dual-arm demonstrations and learns a phase-aware imitation policy for ultrasound-guided interventions. To avoid constraining the operator's natural behavior, DAISS uses a flexible NDI-based leader interface for teleoperating two coordinated follower arms. To support robust execution under real-time ultrasound feedback, we develop a lightweight, data-efficient imitation policy. Specifically, the policy incorporates a phase-aware architecture and a dynamic mask loss tailored to asymmetric bimanual control. Conditioned on a planned trajectory, the network fuses real-time ultrasound with external visual observations to generate smooth, coordinated dual-arm motions. Experimental results show that DAISS can learn personalized expert strategies from limited demonstrations. Overall, these findings highlight the promise of phase-aware imitation-learning-driven dual-arm robots for improving precision and reducing cognitive workload in image-guided interventions.

The pursuit of spatial intelligence fundamentally relies on access to large-scale, fine-grained 3D data. However, existing approaches predominantly construct spatial understanding benchmarks by generating question-answer (QA) pairs from a limited number of manually annotated datasets, rather than systematically annotating new large-scale 3D scenes from raw web data. As a result, their scalability is severely constrained, and model performance is further hindered by domain gaps inherent in these narrowly curated datasets. In this work, we propose Holi-Spatial, the first fully automated, large-scale, spatially-aware multimodal dataset, constructed from raw video inputs without human intervention, using the proposed data curation pipeline. Holi-Spatial supports multi-level spatial supervision, ranging from geometrically accurate 3D Gaussian Splatting (3DGS) reconstructions with rendered depth maps to object-level and relational semantic annotations, together with corresponding spatial Question-Answer (QA) pairs. Following a principled and systematic pipeline, we further construct Holi-Spatial-4M, the first large-scale, high-quality 3D semantic dataset, containing 12K optimized 3DGS scenes, 1.3M 2D masks, 320K 3D bounding boxes, 320K instance captions, 1.2M 3D grounding instances, and 1.2M spatial QA pairs spanning diverse geometric, relational, and semantic reasoning tasks. Holi-Spatial demonstrates exceptional performance in data curation quality, significantly outperforming existing feed-forward and per-scene optimized methods on datasets such as ScanNet, ScanNet++, and DL3DV. Furthermore, fine-tuning Vision-Language Models (VLMs) on spatial reasoning tasks using this dataset has also led to substantial improvements in model performance.

Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature but epistemologically distinct paradigms for PDE solution, classical numerical methods and machine learning approaches, through a unified evaluative framework organized around six fundamental computational challenges. Classical methods are assessed for their structure-preserving properties, rigorous convergence theory, and scalable solver design; their persistent limitations in high-dimensional and geometrically complex settings are characterized precisely. Machine learning approaches are introduced under a taxonomy organized by the degree to which physical knowledge is incorporated and subjected to the same critical evaluation applied to classical methods. Classical methods are deductive -- errors are bounded by quantities derivable from PDE structure and discretization parameters -- while machine learning methods are inductive -- accuracy depends on statistical proximity to the training distribution. This epistemological distinction is the primary criterion governing responsible method selection. We identify three genuine complementarities between the paradigms and develop principles for hybrid design, including a framework for the structure inheritance problem that addresses when classical guarantees propagate through hybrid couplings, and an error budget decomposition that separates discretization, neural approximation, and coupling contributions. We further assess emerging frontiers, including foundation models, differentiable programming, quantum algorithms, and exascale co-design, evaluating each against the structural constraints that determine whether current barriers are fundamental or contingent on engineering progress.

Establishing dense correspondence across 3D shapes is crucial for fundamental downstream tasks, including texture transfer, shape interpolation, and robotic manipulation. However, learning these mappings without manual supervision remains a formidable challenge, particularly under severe non-isometric deformations and in inter-class settings where geometric cues are ambiguous. Conventional functional map methods, while elegant, typically struggle in these regimes due to their reliance on isometry. To address this, we present GLASS, a framework that bridges the gap by integrating geometric spectral analysis with rich semantic priors from vision-language foundation models. GLASS introduces three key innovations: (i) a view-consistent strategy that enables robust multi-view visual feature extraction from powerful vision foundation models; (ii) the injection of language embeddings into vertex descriptors via zero-shot 3D segmentation, capturing high-level part semantics; and (iii) a graph-assisted contrastive loss that enforces structural consistency between regions (e.g., source's head'' $\leftrightarrow$ target's head'') by leveraging geodesic and topological relationships between regions. This design allows GLASS to learn globally coherent and semantically consistent maps without ground-truth supervision. Extensive experiments demonstrate that GLASS achieves state-of-the-art performance across all regimes, maintaining high accuracy on standard near-isometric tasks while significantly advancing performance in challenging settings. Specifically, it achieves average geodesic errors of 0.21, 4.5, and 5.6 on the inter-class benchmark SNIS and non-isometric benchmarks SMAL and TOPKIDS, reducing errors from URSSM baselines of 0.49, 6.0, and 8.9 by 57%, 25%, and 37%, respectively.

Off-world multi-robot exploration is challenged by sparse targets, limited sensing, hazardous terrain, and restricted communication. Many scientifically valuable clues are visually ambiguous and often require close-range observations, making efficient and safe informative path planning essential. Existing methods often rely on predefined areas of interest (AOIs), which may be incomplete or biased, and typically handle terrain risk only through soft penalties, which are insufficient for avoiding non-recoverable regions. To address these issues, we propose a multi-agent informative path planning framework for sparse evidence discovery based on Gaussian belief mapping and dual-domain coverage. The method maintains Gaussian-process-based interest and risk beliefs and combines them with trajectory-intent representations to support coordinated sequential decision-making among multiple agents. It further prioritizes search inside the AOI while preserving limited exploration outside it, thereby improving robustness to AOI bias. In addition, the risk-aware design helps agents balance information gain and operational safety in hazardous environments. Experimental results in simulated lunar environments show that the proposed method consistently outperforms sampling-based and greedy baselines under different budgets and communication ranges. In particular, it achieves lower final uncertainty in risk-aware settings and remains robust under limited communication, demonstrating its effectiveness for cooperative off-world robotic exploration.

Recent advances in Visual-Language-Action (VLA) models have shown promising potential for robotic manipulation tasks. However, real-world robotic tasks often involve long-horizon, multi-step problem-solving and require generalization for continual skill acquisition, extending beyond single actions or skills. These challenges present significant barriers for existing VLA models, which use monolithic action decoders trained on aggregated data, resulting in poor scalability. To address these challenges, we propose AtomicVLA, a unified planning-and-execution framework that jointly generates task-level plans, atomic skill abstractions, and fine-grained actions. AtomicVLA constructs a scalable atomic skill library through a Skill-Guided Mixture-of-Experts (SG-MoE), where each expert specializes in mastering generic yet precise atomic skills. Furthermore, we introduce a flexible routing encoder that automatically assigns dedicated atomic experts to new skills, enabling continual learning. We validate our approach through extensive experiments. In simulation, AtomicVLA outperforms $π_{0}$ by 2.4\% on LIBERO, 10\% on LIBERO-LONG, and outperforms $π_{0}$ and $π_{0.5}$ by 0.22 and 0.25 in average task length on CALVIN. Additionally, our AtomicVLA consistently surpasses baselines by 18.3\% and 21\% in real-world long-horizon tasks and continual learning. These results highlight the effectiveness of atomic skill abstraction and dynamic expert composition for long-horizon and lifelong robotic tasks. The project page is \href{https://zhanglk9.github.io/atomicvla-web/}{here}.

Pretrained Vision-Language-Action (VLA) policies have achieved strong single-step manipulation, but their inference remains largely memoryless, which is brittle in non-Markovian long-horizon settings with occlusion, state aliasing, and subtle post-action changes. Prior approaches inject history either by stacking frames, which scales visual tokens and latency while adding near-duplicate pixels, or by learning additional temporal interfaces that require (re-)training and may break the original single-frame inference graph. We present TempoFit, a training-free temporal retrofit that upgrades frozen VLAs through state-level memory. Our key insight is that prefix attention K/V already form a model-native, content-addressable runtime state; reusing them across timesteps introduces history without new tokens or trainable modules. TempoFit stores layer-wise FIFO prefix K/V at selected intermediate layers, performs parameter-free K-to-K retrieval with Frame-Gap Temporal Bias (FGTB), a fixed recency bias inspired by positional biases in NLP, to keep decisions present-dominant, and injects the retrieved context via pre-attention residual loading with norm-preserving rescaling to avoid distribution shift under frozen weights. On LIBERO-LONG, TempoFit improves strong pretrained backbones by up to +4.0% average success rate while maintaining near-real-time latency, and it transfers consistently to CALVIN and real-robot long-horizon tasks.

Efficient luggage trolley management is critical for reducing congestion and ensuring asset availability in modern airports. Automated detection systems face two main challenges. First, strict security and privacy regulations limit large-scale data collection. Second, existing public datasets lack the diversity, scale, and annotation quality needed to handle dense, overlapping trolley arrangements typical of real-world operations. To address these limitations, we introduce a synthetic data generation pipeline based on a high-fidelity Digital Twin of Algiers International Airport using NVIDIA Omniverse. The pipeline produces richly annotated data with oriented bounding boxes, capturing complex trolley formations, including tightly nested chains. We evaluate YOLO-OBB using five training strategies: real-only, synthetic-only, linear probing, full fine-tuning, and mixed training. This allows us to assess how synthetic data can complement limited real-world annotations. Our results show that mixed training with synthetic data and only 40 percent of real annotations matches or exceeds the full real-data baseline, achieving 0.94 mAP@50 and 0.77 mAP@50-95, while reducing annotation effort by 25 to 35 percent. Multi-seed experiments confirm strong reproducibility with a standard deviation below 0.01 on mAP@50, demonstrating the practical effectiveness of synthetic data for automated trolley detection.